[LeetCode Sync] Runtime - 119 ms (66.46%), Memory - 45.7 MB (57.64%)

Author: NamVr

2562-count-ways-to-build-good-strings/README.md

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+<p>Given the integers <code>zero</code>, <code>one</code>, <code>low</code>, and <code>high</code>, we can construct a string by starting with an empty string, and then at each step perform either of the following:</p>
+
+<ul>
+	<li>Append the character <code>&#39;0&#39;</code> <code>zero</code> times.</li>
+	<li>Append the character <code>&#39;1&#39;</code> <code>one</code> times.</li>
+</ul>
+
+<p>This can be performed any number of times.</p>
+
+<p>A <strong>good</strong> string is a string constructed by the above process having a <strong>length</strong> between <code>low</code> and <code>high</code> (<strong>inclusive</strong>).</p>
+
+<p>Return <em>the number of <strong>different</strong> good strings that can be constructed satisfying these properties.</em> Since the answer can be large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>
+
+<p>&nbsp;</p>
+<p><strong class="example">Example 1:</strong></p>
+
+<pre>
+<strong>Input:</strong> low = 3, high = 3, zero = 1, one = 1
+<strong>Output:</strong> 8
+<strong>Explanation:</strong> 
+One possible valid good string is &quot;011&quot;. 
+It can be constructed as follows: &quot;&quot; -&gt; &quot;0&quot; -&gt; &quot;01&quot; -&gt; &quot;011&quot;. 
+All binary strings from &quot;000&quot; to &quot;111&quot; are good strings in this example.
+</pre>
+
+<p><strong class="example">Example 2:</strong></p>
+
+<pre>
+<strong>Input:</strong> low = 2, high = 3, zero = 1, one = 2
+<strong>Output:</strong> 5
+<strong>Explanation:</strong> The good strings are &quot;00&quot;, &quot;11&quot;, &quot;000&quot;, &quot;110&quot;, and &quot;011&quot;.
+</pre>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</strong></p>
+
+<ul>
+	<li><code>1 &lt;= low&nbsp;&lt;= high&nbsp;&lt;= 10<sup>5</sup></code></li>
+	<li><code>1 &lt;= zero, one &lt;= low</code></li>
+</ul>

2562-count-ways-to-build-good-strings/solution.py

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+class Solution:
+    def countGoodStrings(self, low: int, high: int, zero: int, one: int) -> int:
+        # Use dp[i] to record to number of good strings of length i.
+        dp = [1] + [-1] * (high)
+        mod = 10 ** 9 + 7
+        
+        # Find the number of good strings of length `end`.
+        def dfs(end):
+            if dp[end] != -1:
+                return dp[end]
+            count = 0
+            if end >= zero:
+                count += dfs(end - zero)
+            if end >= one:
+                count += dfs(end - one)
+            dp[end] = count % mod
+            return dp[end]
+            
+        
+        # Add up the number of strings with each valid length [low ~ high].
+        return sum(dfs(end) for end in range(low, high + 1)) % mod